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n-Perfect and \(\mathbb{Q}\)-Perfect Pseudo Effect Algebras

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Abstract

An n-perfect pseudo effect algebra means that it can be decomposed into n+1 comparable slices. We show that such a pseudo effect algebra satisfying a Riesz Decomposition Property type corresponds to the lexicographic product of a cyclic group \(\frac{1}{n}\mathbb{Z}\) with some po-group. The analogous result will be proved for strong \(\mathbb{Q}\)-perfect pseudo effect algebras.

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Acknowledgements

The authors are very indebted to an anonymous referee for his/her careful reading and suggestions which helped us to improve the readability of the paper.

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Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    Anatolij Dvurečenskij

  2. Depart. Algebra Geom., Palacký University, 17. listopadu 1192/12, 771 46, Olomouc, Czech Republic

    Anatolij Dvurečenskij

  3. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, China

    Yongjian Xie

Authors
  1. Anatolij Dvurečenskij
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  2. Yongjian Xie
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Correspondence to Anatolij Dvurečenskij.

Additional information

A.D. has been supported by Slovak Research and Development Agency under the contract APVV-0178-11, the grant VEGA No. 2/0059/12 SAV, and by CZ.1.07/2.3.00/20.0051. Y.X. has been supported by the National Science Foundation of China (Grant No. 11201279), and the Fundamental Research Funds for the Central Universities (Grant No. GK201002037).

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Dvurečenskij, A., Xie, Y. n-Perfect and \(\mathbb{Q}\)-Perfect Pseudo Effect Algebras. Int J Theor Phys 53, 3380–3390 (2014). https://doi.org/10.1007/s10773-013-1723-z

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  • DOI: https://doi.org/10.1007/s10773-013-1723-z

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